因数分解公式

( 1) \(ma+mb-mc=m(a+b-c)\)
( 2) \({a}^{2}+2ab+{b}^{2}={(a+b)}^{2}\)
( 3) \({a}^{2}-2ab+{b}^{2}={(a-b)}^{2}\)
( 4) \({a}^{2}-{b}^{2}={(a+b)(a-b) }\)
( 5) \({x}^{2}+(a+b)x+ab={(x+a)(x+b)}\)
( 6) \(ac{x}^{2}+(bc+ad)x+bd=(ax+b)(cx+d)\)
( 7) \({a}^{3}+{b}^{3}={(a+b)({a}^{2}-ab+{b}^{2})}\)
( 8) \({a}^{3}-{b}^{3}={(a-b)({a}^{2}+ab+{b}^{2}) }\)
( 9) \({a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}={(a+b)}^{3}\)
(10) \({a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}={(a-b)}^{3}\)
(11) \({a}^{4}+{a}^{2}{b}^{2}+{b}^{4}=({a}^{2}+ab+{b}^{2})({a}^{2}-ab+{b}^{2})\)
(12) \({a}^{2}+{b}^{2}+{c}^{2}+2ab+2cb+2ca={(a+b+c)}^{2}\)
(13) \({a}^{3}+{b}^{3}+{c}^{3}-3abc=(a+b+c)({a}^{2}+{b}^{2}+{c}^{2}-ab-cb-ca)\)
(14) \({a}^{2}(b-c)+{b}^{2}(c-a)+{c}^{2}(a-b)=-(b-c)(c-a)(a-b)\)
(15) \(ab(a-b)+bc(b-c)+ca(c-a)=-(b-c)(c-a)(a-b)\)
(16) \({a}^{2}(b+c)+{b}^{2}(c+a)+{c}^{2}(a+b)+2abc=(b+c)(c+a)(a+b)\)
(17) \((a+b+c)(bc+ca+ab)-abc=(b+c)(c+a)(a+b)\)
(18) \({(b-c)}^{3}+{(c-a)}^{3}+{(a-b)}^{3}=3(b-c)(c-a)(a-b)\)
(19) \({(a+b+c)}^{3}-{a}^{3}-{b}^{3}-{c}^{3}=3(b+c)(c+a)(a+b)\)
(20) \({a}^{3}(b-c)+{b}^{3}(c-a)+{c}^{3}(a-b)=-(b-c)(c-a)(a-b)(a+b+c)\)
(21) \(2{b}^{2}{c}^{2}+2{c}^{2}{a}^{2}+2{a}^{2}{b}^{2}-{a}^{4}-{b}^{4}-{c}^{4}=(a+b+c)(b+c-a)(c+a-b)(a+b-c)\)